Pointed Hopf Algebras with classical Weyl Groups

We prove that Nichols algebras of irreducible Yetter-Drinfeld modules over classical Weyl groups $A⋊{\mathbb{S}}_n$ supported by ${\mathbb{S}}_n$ are infinite dimensional, except in three cases. We give necessary and sufficient conditions for Nichols algebras of Yetter-Drinfeld modules over classical Weyl groups $A⋊{\mathbb{S}}_n$ supported by $A$ to be finite dimensional.